3. The owner of a motel is considering outsourcing the daily room cleanup to Duf

Question

3. The owner of a motel is considering outsourcing the daily room cleanup to Duffy’s Maid Service. The manager rents an average of 50 rooms for each of 365 nights. The owner’s cost to clean a room is $12. The Duffy’s Maid Service quote is $18 per room plus a fixed yearly cost of $24,000 for sundry items such as uniforms with the motel’s room. The owner’s fixed cost for space, equipment, and supplies is $60,000 per year.

(a) What is the break-even quantity in terms of the total number of rooms to clean each year?

(b) Which option should be chosen and why?

Explanation / Answer

Number of rooms used per year(Q) = 50 rooms x 365 = 18250 rooms

For insuring, Variable cost (VC) = $12 per room and fixed cost (FC) = $60000 per year

For outsourcing, Variable cost (VC) = $18 per room and Fixed cost (FC) = $24000 per year

a) The break even quantity is the quantity at which both the options will have the same total cost.Let the break even quantity = B. So the break even quantity can be calculated using the following equation

Total cost for insourcing = Total cost for outsourcing

=> FC+(B x VC) = FC+(B x VC)

=> 60000+(B x 12) = 24000 + (B x 18)

=> 60000 + 12B = 24000 + 18B

=> 18B-12B = 60000-24000

=> 6B = 36000

=> B = 36000/6

=> B = 6000

So the break even quantity us 6000 rooms per year

b) Total cost for insourcing = FC + (Q x VC)

= 60000 + (18250 x 12)

= 60000 + 219000

= $279000

Total cost for outsourcing = FC + (Q x VC)

= 24000 + (18250 x 18)

= 24000 + 328500

= $352500

So the option of insourcing the room cleaning should be chosen as it has a lower total cost than outsourcing.

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